You should be able to update using any Live enabled profile logged in when you launch the game. Check your Minecraft folder on your Xbox to see whether the update has already downloaded and you just haven't noticed it. The Xbox Edition is currently at TU16, but this is still only equivalent to a hybrid around the 1.3.1 and 1.4.2 versions on the PC (i.e. still well behind the current PC edition). It could just be that your boys are expecting features that were introduced on the PC later than version 1.3.1 and 1.4.2.
But, when the game is launched, no update prompt appears. (The console is connected to the internet and Xbox Live.)
Do we need an Xbox Gold or other subscription to upgrade? All help appreciated. Many thanks.